Due to process and measurement noise, the robot's true state is unknown. Hence, an estimator maintains a probability distribution over the states, \(x_k \sim b(x_k)\) , called the belief. Note that this is an online estimate conditioned on observed measurements. To conserve communication costs, the system operates with the KF innovation-based ET estimator presented in [1]}, where measurements are only communicated when they are “surprising”. That work derives a recursive minimum mean square error (MMSE) estimator under the assumption that the belief is Gaussian (see Sec. REF  for details). For a given a threshold \(\delta _k \in \Delta = \mathbb {R}_{> 0}\) , measurement \(y_k\)  is surprising if the norm of the Mahalanobis (whitening) transformation of \(z_k = y_k - C \hat{x}_k\)  is larger than threshold \(\delta _k\) .
